Advanced numerical methods for the form finding and patterning of membrane structures

Advanced methods for form finding and patterning of membrane structures are presented based on a consistent nonlinear continuum mechanical formulation. As one of the most general form finding methods, the Updated Reference Strategy is investigated, which is applicable for cables and membranes and for any kind of finite element discretization. The cutting pattern procedure is based on an inverse engineering approach: The yet unknown reference configuration the cutting pattern is modified in such a way, that the difference between the resulting stresses in the final assembled three-dimensional structure and the prescribed stress distribution is minimized. In addition to the individual description of these methods, an extended framework for a detailed analysis and design of membrane structures is presented, whose main focus is to include the influence of the cutting pattern already in the form finding process and structural analysis: Due to the generally existing indevelopability of the spatially curved membrane structure, additional stresses arise in the membrane which have to be included in a detailed modelling of the structure, but have been neglected by conventional approaches.